Steve, You claimed that anything can be expressed mathematically.
Now you say that mathematics is the same as language. Which one- cuneiform, alphabetic, oral, pictographic, hieroglyphic...? No, maths is maths - the likes of 1+3=4 2a+3b=6c and geometric figures and patterns. You ASSUMED that because you use language to do maths – can’t do it without using concepts – they are one and the same. They are demonstrably not. Language existed long, long before maths wh. is only a few thousand years old. The truth is as I said: THERE IS NOT A SINGLE CONCEPT IN THE LANGUAGE THAT CAN BE EXPRESSED MATHEMATICALLY There are only a v. few such as those we just discussed like “add” “subtract” “circle” etc that most people would even *think* to try and express mathematically – and for which there are mathematical notations available (though the maths here is NOT the same as the concepts). In short, the VAST MASS OF LANGUAGE IS OBVIOUSLY NOT MATHEMATICAL –. wh. is why you took about one second flat to respond/ fail to respond to my challenges. You knew as soon as you saw those concepts you didn’t have a hope in hell of expressing them mathematically. And basically you chickened out. And yet to you it was screamingly obvious – unquestionable – that every form of sign system, every form of language – could be expressed mathematically. Your belief was totally divorced from reality – if you care to question that, please go back to the challenges and express those concepts mathematically. You won’t. Many other AGI-ers are similarly deluded – take similar beliefs/delusions about the powers of maths and logic for granted. All this is of extreme importance because we do have to understand how conceptual thought works Conceptual thought is the core of AGI – and broadly it is clear already if you care to look at the science here, along what general lines concepts do work. They are neither mathematical nor logical. Most AGI-ers are simply scientifically ignorant here. Please don’t utter any more rubbish about the powers of maths - unless you want to try and express the concepts I challenged you with. From: Steve Richfield Sent: Friday, August 31, 2012 4:24 PM To: AGI Subject: Re: [agi] How Steve can be creative (or: The Nature of Intelligence/AGI) Mike, On Fri, Aug 31, 2012 at 8:08 AM, Mike Tintner <[email protected]> wrote: You have above three sentences. Please express them mathematically – using any form of mathematical notation. I chose English as my "mathematical" form of expression, and just did what you are asking. Communication in all forms has its "atomic" elements. In a computer it is numbers. Here, it is words. In mathematics, it is symbols. Like subatomic particles, they defy division, but no problem, as there is no need to divide them. When you realise that you do not understand – are deeply confused about – concepts, Sure we don't know how concepts work between our ears. THAT is why we are here discussing it. However, to say that the answer defies any possible form of expression is absurd - at least until you can somehow show that this is somehow true - which you haven't and apparently can't. Steve ======================== From: Steve Richfield Sent: Friday, August 31, 2012 3:32 PM To: AGI Subject: Re: [agi] How Steve can be creative (or: The Nature of Intelligence/AGI) Mike and John, I think part of the problem here is that people aren't underlining critical words in what they are saying, so that messages gets misunderstood. Mike is saying that no presently known mathematical methods can explain GI, and I agree. However, to say that mathematics itself is fundamentally unable to express the workings of GI seems absolutely absurd, because ANYTHING you could possibly understand enough to program can be expressed mathematically - including completely variable mechanisms like self-organization. If Mike is saying that you can't program GI, then he needs to transform his apparent feeling into words that make that point, which so far he has COMPLETELY failed to do. I think Mike means to say that with presently known methods you can't program GI, and I think most of us would agree with THAT. However... The whole reason this forum is here is find ways to blow away the present limitations in math, logic, programming methodologies, etc., whatever they might be, to programming GI. Alternatively, if this is somehow impossible, then that point needs to be proved. A source of long-term mild frustration is the gradual weakening of computer languages. To illustrate, the original Kemeny and Kurtz BASIC started out with matrix operators built into the language, and has gradually gone downhill until .NET has finally stripped out everything that stupid C can't do, so that to my mind, it is nothing of BASIC left. Many early versions of BASIC even allowed the run-time creation and execution of BASIC statements. Some early languages like IT (Internal Translator on the IBM-650) had some wild things, like dynamic equivalence where variables, array elements, and whole arrays could be overlaid in memory as program logic found useful. Many CPUs had indirect addressing, which greatly facilitated having code work on whatever you wanted it to work on. Some machines like the GE/Honeywell 600/6000 series had multi-level indirect addressing, character-level indirect addressing, and many other things like the "Repeat Double" instruction with which you could create your own instructions that would run at hard-wired speeds. All these things subtly shifted the boundary of what it was "programmable". I sense that Mike has fallen into the trap of thinking that a variable refers to a particular thing, e.g. that the value is variable, rather than the item selected being variable, or even an operator in some part of another expression. Of course, arrays provide for the variability in selection, but then people start thinking in arrays rather than in variables. Similarly, Mike thinks that a mathematical expression must refer to the concrete things he thinks variables must refer to, rather than referring to things like the methodology of the creation of other expressions, etc. 808X is not THE worst architecture in history (there WERE some worse ones, e.g. the 4004), but it is definitely in the competition. This has narrowed the minds of an entire generation of programmers. Sure, there are horrendous ways of programming around the absurd limitations of 808X architecture, but they don't teach many of these techniques even in college, because even their need has been forgotten as past generations of programmers go onto Social Security and beyond. Things like dynamic equivalence are nearly zero cost with indirect addressing hardware, but incur severe performance costs on hardware without indirect addressing. Further, it is a hassle to try to write new and advanced systems when you can't even invent the instructions you need to use, but instead must rattle around slow subroutines written using instructions that poorly fit your needs. Hmmm, maybe someone should write a book about what has been lost, both in computer languages and hardware, and in the imaginations of those who are stuck with present software and hardware? Hence, I see Mike's difficulty as a failure of imagination - he can't see what mathematics and computers could do, if freed from their present arbitrary constraints. Any thoughts? Steve =================== On Fri, Aug 31, 2012 at 3:16 AM, Mike Tintner <[email protected]> wrote: John, Quick response because I need to set out what you’ve almost grasped in a fuller, more systematic way, even here. Yours is a v. smart response. What is commonly called language, but should in fact be known as conceptual thinking, is indeed “general high-level thinking” - and is a totally different and separate higher LEVEL of thought to the far lower, specific levels of maths and logic. Steve’s response was v. useful, because it shows that he like most people sees no significant difference between logic, maths and language/conceptual thought – they are more or less “alternatives” to him & our culture – you can use one or the other. Not so. Conceptual thought is totally beyond computers at the moment. It is truly general thought - the essential medium of general intelligence/AGI. If you can’t do concepts you can’t do AGI. And the best demonstration of this is by comparing concepts with their mathematical equivalents. Concepts have vastly, infinitely broad spheres of reference by comparison. A mathematical square is always a mathematical square. A conceptual square can be a square circle or a town square that never was square or a fragmented square or.a square snake .... – and in fact can embrace ***any conceivable deformation and transformation** of the mathematical square. Concepts are multiform/infiniform – mathematical and logical objects are uniform. Concepts enable us to do AGI - to adapt creatively to an everchanging, evernew multiform/infiniform real world. But more later... And my From: John G. Rose Sent: Friday, August 31, 2012 10:58 AM To: AGI Subject: RE: [agi] How Steve can be creative (or: The Nature of Intelligence/AGI) Steve, Your last response to Mike one of the best I’ve seen, generously, thoughtfully and carefully crafted it was a pleasure to read. Unfortunately you were stepping into his trap and wound up here like everyone else. Since Mike is so persistent I’ve tried to grasp what he is saying. My thoughts: 1) People that don’t know math still do math as a general intelligence. 2) The human mind is a powerful mechanism that possibly transcends known mathematics. 3) A typical non-math savvy person is executing advanced mathematics unbeknownst. 4) Mike Tintner is assiduously pointing to these advanced mechanisms, those that are generally and mathematically known, and unknown with much overlap. As AGI’ers we know there are things we can’t figure out. Mike knows that. He’s using his own advanced mathematical execution engine to try to figure out some of the same stuff that we are trying to figure out. Going out on a limb here: Humans have been around for millennia trying to figure out how it all works, the world, humankind, the purpose, the predictions using their own presupplied intelligence engine of the mind without mathematics and computers and have at times in history arrived at “correct” answers to questions that we are still trying to establish the proof of now, scientifically. Scientists are rationality bound, as are engineers. Sometimes there is not a “right” computational model and you can throw Occam’s Razor out the window. A splatting of smattering might cover it then melting away revealing elements of truth underneath a complex explanation for simplicity. John From: Steve Richfield [mailto:[email protected]] Mike, On Thu, Aug 30, 2012 at 3:38 PM, Mike Tintner <[email protected]> wrote: Steve: You failed to respond to my assertion that if you can state it, that it is mathematical (or could easily be turned into mathematical notation paralleling the statement, and then manipulated using rules appropriate to the notation), and if you can't state it, then you can't possibly program it. “Line” ax = by + c “Number” This is atomic to math. “Shape” The interior area of f(x, y) that forms an enclosed area. “form” The constituents of something “Relationship” f where x=f(y) “Add” This is atomic to math. “Subtract” This is atomic to math. “Round” The nearest integer. “Square” To multiply by itself. there isn’t a single CONCEPT that can be stated mathematically. Mathematics is about stating concepts. Or logically. Not a single word in the language. Put down a geometric square and it will not be remotely the same, or have the same infinite sphere of reference, as the *concept* of square. Obviously, we can't discuss concepts until we understand what they are, which is why we need some heavyweight R&D. And your ignorance/lack of imagination re the potential of programming, is comparable to that re conceptual thought – which is the foundation of AGI. Can anyone else on this forum make any sense at all of what Mike has been saying? Steve ======================== AGI | Archives | Modify Your Subscription AGI | Archives | Modify Your Subscription -- Full employment can be had with the stoke of a pen. Simply institute a six hour workday. That will easily create enough new jobs to bring back full employment. AGI | Archives | Modify Your Subscription AGI | Archives | Modify Your Subscription -- Full employment can be had with the stoke of a pen. Simply institute a six hour workday. 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